Cal Poly Mathematics

Math 412-02, Analysis I
Fall 2006

Time: MTRF 9-10
Location: Building 38, Room 201

Instructor: Dr. Ben Richert
Office: Building 25, Room 325
Office phone: (75)6-1681
Office hours: M: 11-12; T: 10-11; R: 10-12; F: 10-11; and by appointment.
Email: brichert@calpoly.edu
Anonymous Feedback Form: http://www.calpoly.edu/~brichert/teaching/412/feedback02.html

Course description: Real analysis is the (major) branch of mathematics which concerns itself with the real numbers and functions of real numbers. Many courses taught at Cal Poly fall into this category (the calculus series, for instance). The difference between this course and those you might have taken earlier, is that previously you were taught the mechanics of using the reals and functions of the reals. The focus was on applications instead of development (in calculus, for instance, this makes sense both because a more rigorous introduction requires a higher level of mathematical maturity and because the audience includes more than just mathematicians). In math 412 (and subsequent courses), we will study the reals and functions of the reals more precisely. The first step, is to tackle the theoretical underpinnings of the ideas introduced in calculus I. For instance, we will carefully develop the reals, limits and sequences, ideas of topology and continuity, and the derivative. Our goal is to prove that these things are well defined and behave as we have been told, and in the process develop the language and proof techniques which make analysis so powerful (which in turn develops the reasoning skills which make a math major so desirable). We could care less (more or less) when two cars will hit each other on the highway if one is traveling north at ... (you get the picture).

Course home page: Access via Blackboard on my.calpoly.edu (or go directly to http://www.calpoly.edu/~brichert/teaching/412/412-02.html)..

Text: Steven Krantz, Real Analysis and Foundations, second edition, Chapman & Hall/CRC Press, 2005.

Syllabus: During the quarter, we will cover chapters 1-7 of the textbook.

Prerequisites: Math 306 or consent of instructor.

Grades: Grades will be based on homework and exams. Each of the homework, the two midterms, and the final counts for 25%. In the computation of your grade, the lower of your two midterm scores will be replaced by the score you received on the final, if that will improve your standing.

Reading: Students are expected to read the section of the text to be covered on a given day before the lecture.

Homework: Homework is the most important part of this course. This is because effectively using the powerful language and methods of proof in analysis takes it practice. Observation helps, but practice is the key - ''Learn by doing'' is absolutely necessary in advanced mathematics courses. Homework will typically be due once per week on Friday. Late homework will not be accepted, but your lowest homework score will be dropped.

Exams: There will be two in-class exams and one cumulative final. Exam 1 is tentatively scheduled for Tuesday, October 24. Exam 2 is tentatively scheduled for Tuesday, November 21. The final will be held from 7-10am on Friday, December 15.